OFFSET
1,4
LINKS
Robert Israel, Table of n, a(n) for n = 1..200
Art of Problem Solving forum, 45th IMO Team Selection Test Lincoln, Nebraska.
FORMULA
For prime p, a(p) = (p-1)*((p-2)^(p-1)-1)/p.
EXAMPLE
For n=4 the a(4)=6 sequences are 0103, 0112, 0301, 3113, 3302 and 3311. - Robert Israel, Aug 30 2020
MAPLE
f:= proc(n)
local g;
g:= proc(i, s) option remember;
if i = 0 then if s=0 then return 1 else return 0 fi fi;
add(procname(i-1, s-k mod n), k= {$0..n-1} minus {2*i mod n, i})
end proc;
g(n, 0)
end proc:
map(f, [$1..30]); # Robert Israel, Aug 30 2020
MATHEMATICA
f[n_] := Module[{g}, g[i_, s_] := g[i, s] = With[{}, If[i == 0, If[s == 0, Return@1, Return@0]]; Sum[g[i-1, Mod[s-k, n]], {k, Range[0, n-1] ~Complement~ {Mod[2i, n], i}}]]; g[n, 0]];
Table[f[n], {n, 1, 30}] (* Jean-François Alcover, May 11 2023, after Robert Israel *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Max Alekseyev, Feb 20 2010
STATUS
approved